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dual 音標拼音: [d'uəl] [d'ul] a. 雙重的,雙的
n. 雙數 雙重的,雙的雙數 dual邏輯被動自動對偶 LPSD
dual自對偶 dual雙 dual adj 1: consisting of or involving two parts or components usually in pairs; " an egg with a double yolk"; " a double ( binary) star"; " double doors"; " dual controls for pilot and copilot"; " duple ( or double) time consists of two ( or a multiple of two) beats to a measure" [ synonym: { double}, { dual}, { duple}] 2: having more than one decidedly dissimilar aspects or qualities; " a double ( or dual) role for an actor"; " the office of a clergyman is twofold; public preaching and private influence"- R. W. Emerson; " every episode has its double and treble meaning"- Frederick Harrison [ synonym: { double}, { dual}, { twofold}, { two- fold}, { treble}, { threefold}, { three- fold}] 3: a grammatical number category referring to two items or units as opposed to one item ( singular) or more than two items ( plural); " ancient Greek had the dual form but it has merged with the plural form in modern Greek" Dual \ Du" al\, a. [ L. dualis, fr. duo two. See { Two}.] Expressing, or consisting of, the number two; belonging to two; as, the dual number of nouns, etc., in Greek. [ 1913 Webster] Here you have one half of our dual truth. -- Tyndall. [ 1913 Webster] 43 Moby Thesaurus words for " dual": Janus- like, ambidextrous, bifacial, bifold, biform, bifurcated, bilateral, binary, binate, biparous, bipartisan, bipartite, bivalent, conduplicate, dichotomous, disomatous, double, double- barreled, double- faced, duadic, dualistic, duple, duplex, duplicate, duplicated, dyadic, geminate, geminated, identical, matched, paired, second, secondary, twain, twin, twinned, two, two- faced, two- level, two- ply, two- sided, two- story, twofold Every field of mathematics has a different
meaning of dual. Loosely, where there is some binary symmetry
of a theory, the image of what you look at normally under this
symmetry is referred to as the dual of your normal things.
In linear algebra for example, for any {vector space} V, over
a {field}, F, the vector space of {linear maps} from V to F is
known as the dual of V. It can be shown that if V is
finite-dimensional, V and its dual are {isomorphic} (though no
isomorphism between them is any more natural than any other).
There is a natural {embedding} of any vector space in the dual
of its dual:
V -> V'': v -> (V': w -> wv : F)
(x' is normally written as x with a horizontal bar above it).
I.e. v'' is the linear map, from V' to F, which maps any w to
the scalar obtained by applying w to v. In short, this
double-dual mapping simply exchanges the roles of function and
argument.
It is conventional, when talking about vectors in V, to refer
to the members of V' as covectors.
(1997-03-16)
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